2023/11/08 by Byeong Guk Go, Go, Byeong Guk, Euijin Jeon +3
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Biological Physics (physics.bio-ph) #Diffusion and Search Dynamics #FOS: Physical sciences #Micro and Nano Robotics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2311.04539
openalex publication_date 2023/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a stochastic process where an active particle, modeled by a one-dimensional run-and-tumble particle, searches for a target with a finite absorption strength in thermal environments. Solving the Fokker-Planck equation for a uniform initial distribution, we analytically calculate the mean searching time (MST), the time for the active particle to be finally absorbed, and show that there exists an optimal self-propulsion velocity of the active particle at which MST is minimized. As the diffusion constant increases, the optimal velocity changes from a finite value to zero, which implies that a purely diffusive Brownian motion outperforms an active motion in terms of searching time. Depending on the absorption strength of the target, the transition of the optimal velocity becomes either continuous or discontinuous, which can be understood based on the Landau approach. In addition, we obtain the phase diagram indicating the passive-efficient and the active-efficient regions. Finally, the initial condition dependence of MST is presented in limiting cases.